Previous |  Up |  Next

Article

Title: On the regulator problem for a class of LTI systems with delays (English)
Author: Castillo-Toledo, Bernardino
Author: Núñez-Pérez, Eduardo
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 39
Issue: 4
Year: 2003
Pages: [415]-432
Summary lang: English
.
Category: math
.
Summary: This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states. We show that conditions for the existence of a solution to this problem (the so-called regulation problem), similar to those known for the case of delay-free linear systems, may be given. We propose a solution for both the state and error feedback regulation. (English)
Keyword: linear systems
Keyword: regulator theory
Keyword: delay systems
MSC: 93B52
MSC: 93C05
MSC: 93C23
idZBL: Zbl 1249.93087
idMR: MR2024523
.
Date available: 2009-09-24T19:55:19Z
Last updated: 2015-03-24
Stable URL: http://hdl.handle.net/10338.dmlcz/135543
.
Reference: [1] Alekal Y., Brunovský P., Chyung D. H., Lee E. B.: The quadratic problem for systems with time delays.IEEE Trans. Automat. Control 16 (1971), 673–687 MR 0308892, 10.1109/TAC.1971.1099824
Reference: [2] Boyd S., Ghaoui L. El, Feron, E., Balakrisnan V.: Linear Matrix Inequalities in System and Control Theory.SIAM Stud. Appl. Math., Philadelphia 1994 MR 1284712
Reference: [3] Chyung D. H.: Tracking controller for linear systems with time delays in both state and control variables.J. of Dyn. Syst. Meas. and Control 115 (1993), 179–183 Zbl 0776.93056, 10.1115/1.2897394
Reference: [4] Francis B. A.: The linear multivariable regulator problem.SIAM J. Control Optim. 15 (1977), 486–505 MR 0446631, 10.1137/0315033
Reference: [5] Hale J. K., Verduyn-Lunel S. M.: Introduction to Functional Differential Equations.Springer–Verlag, New York 1993 Zbl 0787.34002, MR 1243878
Reference: [6] Hautus B. M.: Linear matrix equations with applications to the regulator problem.In: Outils et Modèles Math ématiques pour l’Automatique l’Analyse de Sistèmes et le Traitement du Signal (I. D. Landau, ed.), CNRS, Paris 1983, pp. 399–412 MR 0783851
Reference: [7] Hautus M. L. J.: On the Solvability of Linear Matrix Equations.Memorandum 1982-072, 1988
Reference: [8] Isidori A., Byrnes C. I.: Output regulation of nonlinear systems.IEEE Trans. Automat. Control 35 (1990), 131–140 Zbl 0704.93034, MR 1038409, 10.1109/9.45168
Reference: [9] Kamen E. W., Khargonekar P. P., Tannembaum A.: Stabilization of time-delay systems using finite-dimensional compensators.Trans. Automat. Control 30 (1985), 75–78 MR 0777079, 10.1109/TAC.1985.1103789
Reference: [10] Ni M. L., Er M. J., Leithead W. E., Leith D. J.: New approach to the design of robust tracking and model following controllers for uncertain delay systems.Proc. IEE–D, Control Theory Appl. 148 (2001), 6, 472–477
Reference: [11] Soliman M. A., Ray W. H.: Optimal control of multivariable systems with pure time delays.Automatica 7 (1971), 681–689 Zbl 0242.49025, 10.1016/0005-1098(71)90006-9
Reference: [12] Watanabe K., Nobuyama E., Kitamori, T., Ito M.: A new algorithm for finite spectrum assignment of single-input systems with time delay.IEEE Trans. Automat. Control 37 (1992), 1377–1383 Zbl 0755.93022, MR 1183097, 10.1109/9.159575
Reference: [13] Wonham W. M.: Linear Multivariable Control: A Geometric Approach.Springer–Verlag, New York 1979 Zbl 0609.93001, MR 0569358
Reference: [14] Yen N. Z., Wu Y. C.: Multirate robust servomechanism controllers of linear delay systems using a hybrid structure.Internat. J. Control 60 (1994), 1265–1281 Zbl 0825.93220, MR 1305036, 10.1080/00207179408921520
Reference: [15] Zavarei M., Jamshidi M.: Time Delay Systems.Analysis, Optimization and Applications (North–Holland Systems and Control Series). North Holland, Amsterdam 1987 Zbl 0658.93001, MR 0930450
.

Files

Files Size Format View
Kybernetika_39-2003-4_2.pdf 2.675Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo